NMR study of the diluted magnetic semiconductor alloys Cd1-xMnxSe, Cd1-xCoxSe, and Cd1-xFexSe

Article abstract of DOI:10.1103/PhysRevB.56.6712

Diluted magnetic semiconductors Cd_1-xMn_xSe for x=0.01, Cd_1-xFe_xSe for x=0.01 and 0.02, and Cd_1-xCO_xSe for x = 0.006, 0.009, and 0.01 were studied in the temperature range of 180-400 K by ¹¹³Cd magic-angle-spinning NMR spectroscopy. The NMR spectra of Cd_1-xFe_xSe and Cd_1-xCo_xSe contain a set of resonance lines that are shifted away from the line of the undoped CdSe compound by the transferred hyperfine (THF) interaction between the cadmium nuclei and the paramagnetic ions. The temperature dependence of the THF shifts follows the Curie-Weiss law, and the spin-lattice relaxation times of the shifted lines are significantly shorter than that of the CdSe line. The ¹¹³Cd lines show anisotropies that are smaller than the values evaluated from the dipolar interaction between the paramagnetic ions (M) and their nearest-neighboring cations (M-Se-Cd). The detected anisotropies are therefore composed of dipolar and hyperfine contributions from next-nearest-neighboring (NNN) cadmium nuclei (M-Se-Cd-Se-Cd). The spin-lattice relaxation times of the spectral lines are determined by the electron-nuclear dipolar interaction with NNN cations. The number of observed lines corresponds to the number of nonequivalent NNN cations around each paramagnetic ion. Using the values of the relaxation times and the amplitudes of the lines, it is possible to correlate each line to a well-defined NNN conformation. The NMR spectra of Cd_1-xMn_xSe did not show any fine structure similar to that observed in the Co and Fe alloys.

Full text of DOI:10.1103/PhysRevB.56.6712

PHYSICAL REVIEW B
VOLUME 56, NUMBER 11
15 SEPTEMBER 1997-I
NMR study of the diluted magnetic semiconductor alloys Cd1؊xMn Se, Cd Co Se,
x
1؊x
x
and Cd1؊xFe Se
x
V. Ladizhansky, A. Faraggi, V. Lyahovitskaya, and S. Vega
Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
͑
Received 18 February 1997͒
Diluted magnetic semiconductors Cd1ϪxMn Se for xϭ0.01, Cd Fe Se for xϭ0.01 and 0.02, and
x
1Ϫx
x
1
13
Cd1ϪxCo Se for xϭ0.006, 0.009, and 0.01 were studied in the temperature range of 180–400 K by
Cd
x
magic-angle-spinning NMR spectroscopy. The NMR spectra of Cd1ϪxFe Se and Cd Co Se contain a set of
x
1Ϫx
x
resonance lines that are shifted away from the line of the undoped CdSe compound by the transferred hyperfine
THF͒ interaction between the cadmium nuclei and the paramagnetic ions. The temperature dependence of the
THF shifts follows the Curie-Weiss law, and the spin-lattice relaxation times of the shifted lines are signifi-
͑
1
13
cantly shorter than that of the CdSe line. The
Cd lines show anisotropies that are smaller than the values
evaluated from the dipolar interaction between the paramagnetic ions (M) and their nearest-neighboring
cations (M-Se-Cd). The detected anisotropies are therefore composed of dipolar and hyperfine contributions
from next-nearest-neighboring ͑NNN͒ cadmium nuclei (M-Se-Cd-Se-Cd). The spin-lattice relaxation times of
the spectral lines are determined by the electron-nuclear dipolar interaction with NNN cations. The number of
observed lines corresponds to the number of nonequivalent NNN cations around each paramagnetic ion. Using
the values of the relaxation times and the amplitudes of the lines, it is possible to correlate each line to a
well-defined NNN conformation. The NMR spectra of Cd1ϪxMn Se did not show any fine structure similar to
x
that observed in the Co and Fe alloys. ͓S0163-1829͑97͒06735-0͔
I. INTRODUCTION
113
Cd NMR. It was shown that the different lines in the
Cd NMR spectra of these alloys correspond to cadmium
113
Diluted magnetic semiconductors ͑DMS’s͒ of the form
atoms that are differently coordinated to a paramagnetic ion
and therefore experience different THF interactions. Interac-
tions with nearest-neighbor ͑NN͒ and next-nearest-neighbor
͑NNN͒ cadmium atoms could be distinguished.
II
VI
II
2ϩ
2ϩ
2ϩ
A
M B , with cations A ϭCd , Zn , and Hg , an-
x
1
Ϫx
VI
2Ϫ
2Ϫ
2Ϫ
2ϩ
2ϩ
ions B ϭSe , Te , and S , and MϭMn , Co , and
2
ϩ
Fe substituting part of the cations, have received consider-
able attention in recent years.1 The lattice constants and
band parameters of these ternary DMS alloys can be modi-
fied by varying the concentration of the paramagnetic impu-
–4
Here we report the results of a 113Cd NMR study of the
Cd1ϪxMn Se, Cd Fe Se, and Cd Co Se alloys, pos-
x
1Ϫx
x
1Ϫx
x
4
sessing a wurtzite structure. The zinc-blende structure is cu-
bic, whereas the wurtzite structure is hexagonal. In the zinc-
blende and wurtzite crystals, a paramagnetic ion, replacing a
cadmium ion in the lattice, has 12 NN cations, located at
rities. The presence of the paramagnetic ions can yield inter-
esting magnetic properties.2
,4–10
For example, large
concentrations of paramagnetic impurities result at low tem-
peratures in the formation of spin-glass-like states.1 These
and other magnetic properties are related to long-range ex-
change ͑superexchange͒ interactions that are mediated by the
spin polarization of the electron density distributions be-
tween the paramagnetic ions. The magnitudes of these inter-
actions are strongly dependent on the lengths and angles and
on the covalence strengths and the orbital hybridizations of
the bonds connecting the paramagnetic impurities.13,14
Another type of magnetic interaction that exists in the
DMS alloys is the transferred hyperfine ͑THF͒ interaction
between the unpaired electrons of the magnetic ions and the
nuclear spins of the nonmagnetic atoms. This interaction can
be monitored by NMR spectroscopy. Since the THF interac-
tion is also mediated by spin polarization of electronic orbit-
als, a better understanding of the dependence of this interac-
tion on the bond properties of the interacting atoms can
provide information about the electronic mechanism govern-
ing the superexchange.
1,12
VI
sites that are two bonds (M-B -Cd) away. In the zinc-
blende structure the 12 NN sites are all related crystallo-
graphically. In the wurtzite three sets of sites, not related by
crystal symmetry, can be distinguished: 6 ‘‘in-plane’’ sites,
3 ‘‘above-the-plane’’ sites, and 3 ‘‘below-the-plane’’ sites.
The 12 cadmium atoms at these sites are all equidistant to the
central ion.
The zinc-blende and wurtzite structures differ signifi-
cantly, when the bond structures between a center ion and its
NNN cations are considered. The 42 NNN atoms in the zinc-
blende lattice can be classified according to 4 nonequivalent
bond structures. They can be characterized by trans-trans
(tt), gauche-trans (gt), trans-gauche (tg), and gauche-
gauche (gg) conformations.16 In the wurtzite structure there
are 44 NNN cadmium atoms, which must be divided into 11
conformations. Each conformation is characterized by four
bonds (M-Se-Cd-Se-Cd) and can be defined by the dihedral
angles of the third and fourth bonds starting from M. In this
terminology the tg conformation is assigned by ͑180°, 60°͒
and the tt conformation by ͑180°, 180°͒. Table I summarizes
the 4 sets of NNN cadmium sites in the zinc-blende structure
The transferred hyperfine interactions in the alloys
Cd1ϪxMn Te ͑Ref. 15͒ and Cd Fe Te ͑Ref. 16͒, exhibit-
x
1Ϫx
x
ing a zinc-blende structure, have already been studied by
0
163-1829/97/56͑11͒/6712͑7͒/$10.00 56
6712
© 1997 The American Physical Society

56
NMR STUDY OF THE DILUTED MAGNETIC . . .
6713
TABLE I. Bond conformations, number of sites, and distances
between the paramagnetic ion (M) and the cadmium atoms of NNN
cation configurations in wurtzite CdMSe and zinc-blende CdMTe.
ning speeds of the samples. In Sec. II the sample preparation
procedure is described and the parameters of the NMR ex-
periments are given. In Sec. III the 1 Cd MAS NMR spectra
13
of the Cd1ϪxM Se samples are presented and discussed, and
x
Distance
͑Å͒
in Sec. IV the results are summarized. As will be shown, an
assignment of the spectral lines to the conformations I to XI
can be made that is based on the analysis of the relaxation
times and intensities of the lines.
Conformations in CdMSe
͑180°,180°͒
͑120°,180°͒
͑180°,120°͒
Number of sites
I
II
III
6
6
6
3
3
6
6
1
1
3
3
8.6
8.2
8.2
7.5
7.5
7.5
7.5
7.0
7.0
6.1
6.1
IV (180°,60°)ϩ(180°,Ϫ60°)
(Ϫ60°,180°)ϩ(60°,180°)
VI (Ϫ60°,180°)ϩ(Ϫ60°,Ϫ120°)
VII (180°,Ϫ60°)ϩ(Ϫ120°,Ϫ60°)
VIII ͑180°,0°͒
II. EXPERIMENTAL DETAILS
A. NMR measurements
V
The NMR experiments were performed using a home-
built 200-MHz NMR spectrometer, a Bruker 300-MHz CXP
IX ͑0°,180°͒
or a Bruker 300-MHz DSX NMR spectrometer. The Larmor
X
(60°,60°)ϩ(Ϫ60°,Ϫ60°)
XI (Ϫ120°,60°)ϩ(60°,60°)ϩ
Ϫ60°,Ϫ60°)ϩ(120°,Ϫ60°)
113
frequencies of
Cd in these spectrometers are equal to
4
4.37 and 66.55 MHz, respectively. All measurements were
performed on samples rotating in the external magnetic field
at the magic angle. The spin-echo sequence ␲/2-␶-␲-␶-
acquisition was used for the detection of the signals in all
experiments. The length of the ␲/2 pulse varied from 3 to 4
sec, and the delay time ␶ was always equal to the length of
(
͕
Distance
͑Å͒
͖
Conformations in CdMTe
Number of sites
͑
͑
͑
͑
180°,180°͒
12
12
12
6
9.2
7.9
7.9
6.5
␮
180°,60°͒, (180°,Ϫ60°)
60°,180°͒, (Ϫ60°,180°)
60°,60°͒, (Ϫ60°,Ϫ60°)
one rotor period. High-speed 5- and 7-mm and standard
7-mm MAS probes of Doty Scientific Inc. were used and the
experiments were performed between 180 and 400 K. The
spinning speeds of the samples varied from 2 to 7.5 kHz,
with a stability of 30 Hz, and a Bruker variable-temperature
unit W110512 provided a temperature stability of Ϯ0.2 K.
Spin-lattice relaxation times of 1 Cd nuclei were mea-
and the 11 NNN sets in the wurtzite structure. In part of the
configurations two or four pathways are present simulta-
neously. The 11 sets of cadmiums are numbered from I to
XI. The 11 types of cadmiums can result maximally in 11
13
sured using the saturation recovery sequence
͕ ͖
␲/2-t n
-
T-␲/2-␶-␲-␶-acquisition. In these experiments the ampli-
tudes of the lines were monitored as a function of T and
fitted to single exponents.
1
13
THF shifted
Cd NMR lines with intensities proportional
to the number of sites in each conformational set.
The NN superexchange integrals of Cd-based zinc-blende
and wurtzite alloys Cd1ϪxMn Te, Cd1ϪxMn Se, and
x
x
B. Sample preparation
4
Cd1 Mn S are all of the order of (7Ϯ3) K. Shapira
Ϫx
x
1
7
et al. have recently shown that in the wurtzite crystals the
Cd1ϪxMnxSe, Cd1ϪxCoxSe, and Cd1ϪxFexSe polycrystal-
line samples were prepared for x values between 0.003 and
0.05. First the MSe binary compounds with MϭMn, Co,
and Fe were synthesized. This was accomplished by mixing
pure M and Se in a molar ratio of 1:1.1 and by evacuating
NN superexchange interactions between Mn ions occupying
‘‘in-plane’’ sites are different from those occupying ‘‘out-of-
plane’’ sites. The direct Mn-Se-Mn bond conformation is
identical for the in-plane and out-of-plane paramagnetic ion
pairs, and it was argued that the differences in the NN su-
perexchange constant result from differences between the ad-
ditional polarization paths, involving four bonds. For ex-
ample, the four-bond pathway Mn-Se-Cd-Se-Mn between
the out-of-plane neighbors has a ͑0°, 60°͒ or ͑60°, 0°͒ con-
formation, while the pathway between in-plane neighbors is
of the ͑60°, 60°͒ type.
Ϫ5
the mixture in quartz ampoules to 10 Torr. The sealed
ampoules were then heated at a rate of 50 °C/h up to 850 °C
and kept at that temperature for 3 days, after which they were
annealed at 1000 °C. The resulting MSe compounds were
mixed with CdSe in appropriate molar ratios, thoroughly
milled in an agate mortar, and loaded into carbon-coated
quartz ampoules. These ampoules were also sealed in a
Ϫ5
The spin polarization of the different path ways varies,
yielding different superexchange constants. Since the THF
interaction strength is also dependent on the polarization
transfer through the bonds, the assignment of the bond con-
formations to the experimental THF coupling constants con-
tributes to the understanding of the role of the path way in
the superexchange interaction. Thus the objective of this
study is to find the correlations between the THF coupling
constants and the bond conformations in the wurtzite alloys.
In the following sections we discuss the magic angle spin-
vacuum of 10 Torr and sintered at 1000–1100 °C for 10
days. To improve the homogeneity of the distribution of im-
purities for small x values (xϽ0.01), the sintered polycrys-
talline ingots were milled and annealed a second time.
All samples were checked and characterized by energy-
dispersive ͑x-ray fluorescence͒ spectroscopy ͑EDS͒ and by
x-ray photoelectron spectroscopy ͑XPS͒. For our experi-
ments we used only samples that were single-phase com-
pounds with homogeneously distributed magnetic ions. The
measured concentrations were in good agreement with those
expected from the preparation procedure, their values vary-
ing by less than 5%.
1
13
ning ͑MAS͒ Cd NMR experiments on Cd1ϪxM Se alloys
x
with various values of x at different temperatures and spin-

6714
LADIZHANSKY, FARAGGI, LYAHOVITSKAYA, AND VEGA
56
FIG. 2. 113Cd MAS NMR spectra of the alloys ͑a͒
Cd0.02Fe0.98Se, ͑b͒ Cd0.99Fe0.01Se, ͑c͒ Cd0.991Co0.009Se, and ͑d͒
Cd0.994Co0.006Se. The experimental parameters of the measurements
were the same as for Fig. 1, except that the repetition time of the
experiments on the Fe alloys was 600 msec and of the Co alloys
was 300 msec, and the number of accumulations was 24 000.
FIG. 1. 113Cd MAS NMR spectra of the alloys ͑a͒
Cd0.99Mn0.01Se, ͑b͒ Cd0.99Fe0.01Se, and ͑c͒ Cd0.99Co0.01Se. The
spectra are the Fourier transformation of the spin-echo signals, ob-
tained at a spinning speed of 7.5 kHz and at a Larmor frequency of
3
00 msec, and on Cd1ϪxFe Se samples, with xϭ0.01 and
x
0.02, with a repetition time of 600 msec. Figure 2 presents
the results of these experiments obtained after 24 000 accu-
mulations. The spectral features of the Co and Fe samples
are very similar, and the relative peak heights of the low-
intensity lines of the two Cd1ϪxCo Se samples are about
equal, as is the case for the Cd1ϪxFe Se samples.
These results indicate that the low-intensity lines have
shorter relaxation times than the main line and that their
relative intensities seem to be independent of the concentra-
tion of the paramagnetic ions. Their intensities with respect
to the main line increase for increasing x values. The differ-
ence between the spectra of the Mn and Co/Fe alloys could
be due to a difference between the electronic relaxation times
of these ions in the alloys. This possibility is discussed in the
forthcoming text.
4
4.37 MHz, after 3600 accumulations. The time between the rf
pulses was 133 ␮sec and the repetition time was 15 sec. The 0 ppm
positions were chosen at the maximums of the main CdSe lines.
The low-intensity parts of the spectra are emphasized by multiply-
ing the spectra by factors indicated in the figure.
x
x
III. NMR RESULTS
A. Spectral line positions
Figure 1 shows the 113Cd MAS NMR spectra of the
samples Cd1ϪxMn Se for xϭ0.01, Cd Fe Se for x
x
1Ϫx
x
ϭ0.01, and Cd1ϪxCo Se for xϭ0.009. These results were
x
Following the previous 1 Cd NMR studies15,16 of alloys
with a zinc-blende structure, we assumed that the shifted
frequency bands correspond to the cadmium nuclei differ-
ently coordinated to the paramagnetic impurities. To demon-
strate that the line shifts are governed by the THF interac-
tion, we recorded 1 Cd spectra at different temperatures.
Figure 3 illustrates the inverse temperature dependence of
the shifts of six lines in the spectra of Cd0.99Co0.01Se and
Cd0.99Fe0.01Se. The shifts follow the Curie-Weiss law, con-
firming that they result from the hyperfine interaction be-
tween nuclear spins and paramagnetic ions.
13
obtained after Fourier transformation of the spin-echo signals
of samples spinning at a rotor speed of 7.5 kHz. In these
experiments 3600 echoes were accumulated with a repetition
time of 15 sec. The spectra exhibit a set of low-intensity
lines in addition to the main peaks. The main peak in each
spectrum is located at the position of the 1 Cd line of pure
CdSe and is chosen as the 0 ppm reference. The multifre-
quency spectral features were only obtained from Co and Fe
samples; the Mn samples showed only a very small spectral
line at 176 ppm in addition to the CdSe line. To assure that
these differences did not depend on our synthesis, we per-
13
13
1
13
formed
Cd NMR of Cd1ϪxMn Se samples, not prepared
x
At the high-temperature approximation (B /TӶ1), the
0
1
8
113
by us. Also, in these samples no shifted
detected. The same is true in
Cd1ϪxMn S alloys.
Cd lines were
Cd spectra of wurtzite
shift of each set of equivalent cadmium nuclei is given by
113
19
x
A
g␮ S͑Sϩ1͒B0
B
Spin-echo experiments were repeated on Cd1ϪxCo Se
⌬␯ ϭ
ϩ⌬␯0i ,
͑1͒
x
i
ͫ ͬ
h i
3kBT
samples, with xϭ0.006 and 0.009, with a repetition time of

56
NMR STUDY OF THE DILUTED MAGNETIC . . .
B. Relaxation time measurements
6715
The spin-lattice relaxation rate of a cadmium spin belong-
ing to the ith conformational set of cations has two
contributions2
1,22
1
2
1
2
3␶
7␶
2
2
ͫ
ͬ
ϭ
S͑Sϩ1͒g ␮B␥I
6
ͫ
2 ϩ
1ϩ͑␻ ␶͒2
ͬ
T1 i 15
Ri 1ϩ͑␻ ␶͒
I
S
3
A 2
␶
ϩ
S͑Sϩ1͒ͫ ͬ
.
͑2͒
2
h i 1ϩ͑␻ ␶͒2
S
The first term is due to fluctuations of the dipolar interaction
between the magnetic moment of a paramagnetic ion and the
nuclear cadmium spin, and the second term is due to the
THF interaction. ␥ is the nuclear magnetogyric ratio, R is
I
i
the distance between the paramagnetic ion and the cadmium
atom in the ith configuration, ␶ is the electron spin-lattice
relaxation time of the paramagnetic ion, ␻ is the electronic
S
Larmor frequency, and ␻ is the nuclear Larmor frequency.
I
8
In a field of 4.7 T we obtain that ␻ ϭ2.8ϫ10 rad/sec and
I
1
1
21
␻Sϭ9.5ϫ10 rad/sec, and for typical ␶ values
of
and 10 sec for
Mn , ␻ ␶Ͻ1 and ␻ ␶у1. For distances RNNϭ4.3 Å and
Ϫ12
Ϫ11
2ϩ
2ϩ
Ϫ9
1
0
–10
sec for Co
and Fe
2ϩ
I
S
RNNNϭ6.1–8.6 Å between a paramagnetic ion and its NN
and NNN cadmium nuclei in the Cd1ϪxM Se crystal, respec-
x
tively, the dipolar contributions to 1/T for the NN cadmium
1
atoms in the Co and Fe alloys are of the order of
FIG. 3. Inverse temperature dependence of the shifts of six cad-
1
2
Ϫ1
Ϫ1
1
1
0 –10 sec
and for the NNN cadmium atoms
mium lines in the MAS spectra of ͑a͒ Cd0.99Fe0.01Se and ͑b͒
Cd0.99Co0.01Se. The straight lines through the experimental points
are least squares fits. The THF interaction constants in Table II
were derived from the slopes of these lines.
Ϫ1
0
–10 sec . The largest THF contribution to the relax-
ation rate that can be expected, when we consider the largest
hyperfine coupling constant A/h in Table II and a small ␶
Ϫ12
Ϫ1
value of 10
sec, is of the order of 1 sec . From these
where B0 is the external magnetic field, ⌬␯0i is the
temperature-independent chemical shift contribution to
considerations it follows that the main contribution to the
1/T1 value comes from its dipolar term.
⌬
␯ , and ͓A/h͔ is the strength of the hyperfine interaction
T1 relaxation times were measured by performing satura-
tion recovery experiments. In Table III the experimental re-
i
i
experienced by the ith set of cadmium nuclei. The values of
the hyperfine coupling constants can be extracted from the
113
laxation times of seven lines in the
Cd spectrum of
slope of ⌬␯ (1/T). Table II summarizes these values and the
Cd0.994Co0.006Se are presented. They were derived from a
single-exponential best-fitting procedure. In addition to the
relaxation times, the relative line intensities of the fully re-
laxed spectrum were also obtained. The relaxation times of
the lines at 77 and 115 ppm could not be determined and
only an upper limit for their values can be given. These lines
sit on top of a broad spectral feature, with a long spin latice
relaxation time, close to the main line of the spectrum.
The T1 values vary between 100 and 600 msec. The line
at 515 ppm with the largest A/h constant has a T1 value of
about 100 msec. If we assume that the relaxation time of that
i
isotropic chemical shifts ⌬␯0i of six lines in the
Cd0.99Co0.01Se and Cd0.99Fe0.01Se alloys. These experiments
were performed at a B field of 4.7 T. The ͓A/h͔ values
0
i
were derived using g values of 2.29 ͑Ref. 20͒ and 2.3 ͑Ref.
ϩ
2ϩ
1
0͒ and S values of 1.5 and 2 for Co2 and Fe , respec-
tively. The absolute values of the THF coupling constants
vary from 0.1 to 0.6 MHz. In the Fe alloys the chemical shift
contributions are about zero, whereas in the Co alloys they
follow the magnitudes of the hyperfine constants and vary
from 120 to Ϫ30 ppm.
TABLE II. Transferred hyperfine interaction constants of Cd1ϪxFe Se and Cd Co Se.
x
1Ϫx
x
Cd1ϪxFe Se
Cd1ϪxCo Se
x
x
⌬␯ ͑ppm͒
A/h ͑MHz͒
⌬␯ ͑ppm͒
⌬␯ ͑ppm͒
A/h ͑MHz͒
⌬␯ ͑ppm͒
0
0
544
423
348
178
104
0.47
0.37
0.32
0.15
0.08
29
14
Ϫ9
18
515
367
290
158
77
0.58
0.43
0.32
0.19
0.18
118
74
70
34
50
17
Ϫ102
Ϫ0.09
Ϫ3
Ϫ121
Ϫ0.13
Ϫ27

6716
LADIZHANSKY, FARAGGI, LYAHOVITSKAYA, AND VEGA
56
TABLE III. Spin-lattice relaxation times and fully relaxed intensities of the 113Cd lines of
Cd0.994Co0.006Se and the assignment of these lines to the sets of conformations I–XI with the number of sites
and their theoretical T relaxation times.
1
T ͑msec͒
͑experimental͒
Intensities
͑arbitrary units͒
Total number
of sites
T ͑msec͒
͑theoretical͒
1
1
⌬
␯ ͑ppm͒
Assignment
5
3
2
1
1
15
67
90
58
15
105Ϯ15
135Ϯ15
165Ϯ40
325Ϯ95
Ͻ260
55Ϯ5
20Ϯ3
64Ϯ9
105Ϯ15
Ͻ30
Ͻ100
XϩXI
VIIIϩIX
VII
VϩVI
IV
6
2
6
9
3
103
235
356
356
356
809
608
7
7
Ͻ600
470Ϯ100
I
6
12
Ϫ121
150Ϯ25
IIϩIII
line is fully determined by the first term in Eq. ͑2͒ and that
this line belongs to cadmium nuclei at distances RNN
ϭ4.3 Å or RNNNϭ6.1–8.6 Å, then the correlation time ␶
speed and the temperature. The relative intensities of the
sidebands and center bands are influenced by the anisotropic
parts of the chemical shift and the dipolar and THF interac-
tions. Figure 4 shows two representative slow-spinning MAS
spectra of Cd0.994Co0.006Se obtained at different tempera-
tures. The differences between these spectra indicate that the
cadmium nuclei experience significant temperature-
dependent anisotropic interactions. The relative contributions
of the different interactions to the anisotropy are unknown.
However, we will show that the dipolar contribution can pro-
vide us with the necessary information to conclude that the
THF shifts in the spectra originate from interactions with
NNN atoms.
Ϫ12
Ϫ11
Ϫ10
becomes 2.6ϫ10
sec or 2.2ϫ10 –1.8ϫ10
sec, re-
spectively. For the same distances the ␶ value of the line at
Ϫ13
Ϫ121 ppm becomes 4.4ϫ10
sec or falls in the range
Ϫ12
Ϫ11
3.6ϫ10 –2.9ϫ10
sec, respectively. In the next section
we will show that the low-intensity lines correspond to NNN
cadmium atoms. Therefore it seems right to conclude that the
Ϫ11
electronic relaxation time is about 2.5ϫ10
sec.
There must exist a significant difference between at least
part of the spectral parameters of the Cd1ϪxFe Se and
x
Cd1ϪxCo Se alloys and the Cd Mn Se alloys. While the
x
1Ϫx
x
Co and Fe alloys exhibit a set of low-intensity lines, the Mn
alloys for a variety of x values did not show any of these
lines. A possible explanation for this difference may be that
Noting that the anisotropies of the different interactions
have an additive effect on the sideband patterns, we shall
restrict ourselves by considering only the dipolar contribu-
tion to the anisotropy. The value of the expected anisotropy
of the dipolar interaction between a paramagnetic ion and a
cadmium nucleus can be evaluated by calculating the high-
temperature average magnetic moment of this ion,
the T values of the NNN cadmium nuclei in the Mn alloys
2
are smaller than in the other alloys. The expression for the
spin-spin relaxation rate of a cadmium spin contains a dipo-
lar term and a term governed by the THF interaction, just as
2
1,22
for 1/T1 .
1T,2h2e dipolar term of the ith configurational set
2
2
͑g␮ ͒ S͑Sϩ1͒
B
has the form
͗
␮
͘
ϭ
B0 .
͑4͒
3
k T
B
2
2
2
1
␥ ␥ h
13␶
3␶
With Sϭ1.5 and gϭ2.29 for Co2ϩ, the value of ͗␮͘ becomes
0.104␮B in an external magnetic field of 7.05 T and at a
temperature of 300 K. The dipolar anisotropy ⌬␯dip
I
S
ͫ
ͬ
ϭ
15R6i
S͑Sϩ1͒
ͭ
4␶ϩ
2 ϩ
1ϩ͑␻ ␶͒2
ͮ
.
T2
1ϩ͑␻ ␶͒
S
I
i
͑3͒
According to this expression, the T values of the NNN cad-
2
miums in the Co alloys are in the range of 70–570 msec,
Ϫ11
when ␶ϭ2.5ϫ10
sec. For the Mn alloys the spin-spin
relaxation times become about 1–8 msec, when we assume
Ϫ9
23
that ␶ϭ10 sec. These values cannot be the reason for
2ϩ
the disappearance of all the THF-shifted lines. Mn elec-
tronic correlation times longer than 10 sec are necessary
Ϫ8
to explain the fact that the free induction decay signals of the
THF-shifted cadmium nuclei are too short to be detected. In
the case of the zinc-blende Cd1ϪxMn Te alloys, the cad-
x
mium T values are long enough to allow the observation of
2
15
the THF shift lines. This fact may be related to the differ-
ences between the zinc-blende and wurtize crystal structures.
C. Anisotropic contributions
FIG. 4. Two typical slow spinning 113Cd MAS NMR spectra of
Cd0.994Co0.006Se. These spectra were obtained from experiment
with a repetition time of 300 msec after 24 000 accumulations.
To investigate which bond conformations cause the THF
shifts in the cadmium spectra, we studied the MAS sideband
patterns of the spectral lines as a function of the spinning

56
NMR STUDY OF THE DILUTED MAGNETIC . . .
6717
Ϫ3
relaxation times are somewhat smaller than the theoretical
ϭ␥I
͗
␮
͘
R
of a NN cadmium nucleus, interacting with a
NN
2
ϩ
ones, but their values follow the expected changes due to the
Co at a distance RNNϭ4.3 Å in Cd1ϪxCo Se, is 11.7 kHz.
x
6
changes in R
.
With the same parameters the dipolar anisotropy of a NNN
cadmium nucleus at a distance of 6.1 Å from the Co2 ion
becomes 4.1 kHz. In the Fe alloys the dipolar anisotropies
are somewhat larger.
NNN
ϩ
IV. SUMMARY
The presence of the paramagnetic ions in the CdSe DMS
samples causes significant changes in the 1 Cd MAS NMR
spectra. Well-resolved shifted lines with short relaxation
times were observed in the Co- and Fe-based alloys. From
the temperature studies and anisotropy measurements, we
concluded that the shifts are caused by the THF interaction
between the paramagnetic ions and their NNN cadmium nu-
clei. An assignment of the 1 Cd lines of Cd0.994Co0.006Se to
the sets of NNN cations with specific bond configurations
was made by comparing experimental line intensities and
13
We measured the sideband intensities of the various cad-
mium lines in Cd0.994Co0.006Se as a function of temperature,
spinning speed, and magnetic field ͑experiments were per-
formed at 4.7 and 7.05 T͒. Spectral overlap of the sideband
patterns, poor signal-to-noise ratios and the fact that at low
temperatures the lines broaden significantly made it all diffi-
cult to perform an accurate Herzfeld-Berger analysis24 of the
MAS patterns. However, we were able to determine that the
values of the anisotropy parameter ⌬␯dip of all detectable
sideband patterns were in the range of 4.8Ϯ2 kHz at room
temperature and 8.0Ϯ2.5 kHz at Tϭ200 K. Because the ex-
13
relaxation times with the number of cations in these sets and
6
their T1 values calculated using their R
values. The
NNN
1
13
perimental
Cd anisotropies of the Cd1ϪxCo Se alloys are
x
strongest THF interaction occurs between a paramagnetic
2ϩ
clearly smaller than 11.7 kHz at room temperature and
smaller than 17.5 kHz at Tϭ200 K, we must conclude that
the THF-shifted lines correspond to NNN cadmium atoms.
Almost all sideband patterns had an asymmetry parameter of
about 0.1. The presence of the asymmetry indicates that the
dipolar interaction is not the only contribution to the aniso-
tropic parts of the spectra.
Co and its NNN cations at a distance 6.1 Å and with a
Ϯ60°,Ϯ60°)ϩ(Ϯ120°,Ϯ120°) configuration. The value
(
of the THF interaction is negative when the NNN cations are
2ϩ
removed from the Co ion by 8.2 Å and have a ͑120°, 180°͒
bond configuration. The smallest value is found for the all-
trans configuration. These results show the dependence of
the THF coupling constants on the type of bond conforma-
tion. It is interesting to notice that there exists some correla-
tion between the magnitudes of the THF constants and the
distances between interacting spins. In future work the de-
pendence of the THF interaction on these bond properties
should be studied theoretically by evaluating the electronic
spin polarizations in the crystal. Additionally, the values of
the electronic correlation times in the different alloys should
be evaluated in order to explain the relaxation data. The data
presented in this paper can also be used as a tool for the
determination of the incorporation of paramagnetic ions in
DMS micro- and nanoparticles.
D. Line intensities
In order to make an assignment of the spectral lines in
Figs. 1 and 2 and correlate them to the 11 sets of NNN
conformations, the relative intensities of these lines in their
fully relaxed spectrum must be compared with the number of
cadmium atoms in each set ͑see Table I͒. In addition we
expect that the values of the T1 relaxation times of these
lines are proportional to R
Eq. ͑2͒. In Table III an assignment of the lines is suggested
based on a comparison of the experimental line intensities
and the magnitudes of their spin-lattice relaxation times with
the numbers of cations in the conformational sets I–XI and
their theoretical T values, respectively. The theoretical T ’s
6
, according to the first term in
NNN
ACKNOWLEDGMENTS
1
1
The authors want to thank Professor W. Giriat for supply-
ing DMS samples and Professor W. J. M. de Jonge and Dr.
H. J. M. Swagten for stimulating discussions and advice re-
garding the analysis of our data. We wish to express our
appreciation for the stimulating discussions with Dr. D.
Zamir and his encouragement to continue the work. Part of
this work was supported by the Minerva Foundation.
were calculated using the dipolar term of Eq. ͑2͒ with ␶
Ϫ11
6
ϭ2.5ϫ10
sec and the R
values of the assigned con-
NNN
figurations. Realizing that the signal to noise of the spectra is
rather poor and the fact that part of the spectral features
overlap, the agreement between the experimental values and
the calculated parameters is satisfactory. Most experimental
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